Question

Show that 6^n can be never end with zero

Answer 1

Every positive integer ending with zero , also divisible by 5, and hence it prime factorisation must contains the 5
Now we have,
6^n
The prime factorisation is, 2 and 3
There is no other prime factors other than 3 and 2
By the uniqueness of fundamental arithmetic
It's prove that it can't end with 0

Answer 2

6^1=6
6^2=36
6^3=216.......
so it follows a certain pattern
so 6^n cannot end with zero